Question

an oval track is made by erecting semicircles on each end of a 48 m by 96 m rectangle. Find the length of the track and the area enclosed by the track.

Answer 1

Let's make a diagram to represent the problem

To find the length of the track, we have to find the circumference of both semi-circles, which form 1 circle

`C=\pi d=3.14\cdot48\approx150.72m`

Then, we add both lengths of the rectangle.

`P=150.72+96+96=342.72m`

The length of the track is 342.72 m, approximately.

Now, we have to find the area of the circle and the area of the rectangle

`\begin{gathered} A_{\text{circle}}=\pi(r)^2\approx3.14\cdot(24m)^2\approx1,808.64m^2 \\ A_{\text{rectangle}}=l\cdot w=96m\cdot48m=4,608m^2 \end{gathered}`

Then, we add the areas

`A_{\text{track}}=1,808.64m^2+4,608m^2=6,416.64m^2`

The area of the track is 6,416.64 square meters.